CN109408986B - Design method of elliptical beam Cassegrain antenna - Google Patents
Design method of elliptical beam Cassegrain antenna Download PDFInfo
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Abstract
The invention discloses a design method of an elliptical beam Cassegrain antenna, and belongs to the technical field of satellite communication antenna design. The method comprises parameterization of an orofacial field function and a transition function; forming population individuals by parameters of the mouth-face field function and the transition function, and performing population iteration based on a DEGL algorithm; and shaping the antenna by using the optimal individuals in the population of the last generation to obtain the optimal design of the elliptic wave beam Cassegrain antenna. The method can rapidly optimize and design the elliptical beam antenna with high efficiency, low side lobe, low cross polarization and large axial ratio, and is an important improvement on the existing antenna design method.
Description
Technical Field
The invention relates to the technical field of satellite communication antenna design, in particular to a design method of an elliptical beam Cassegrain antenna. The invention can be used for designing high-performance and low-profile antennas for mobile satellite stations, particularly satellite communication stations with limited space such as satellite-borne, vehicle-mounted and airborne antennas.
Background
In the field of satellite communication, the technology of shaped dual-reflector antenna is the mainstream direction of current research. The shaped elliptical beam cassegrain antenna has attracted attention because it can form a large axial ratio elliptical beam, and realize low profile and high efficiency.
At present, in the design of a shaped elliptical beam cassegrain antenna, an aperture surface field and a transition function are key elements of the design. The conventional classical oral surface field has the forms of generalized Taylor displacement distribution, exponential distribution, hansen distribution and the like, but the forms are only suitable for circular aperture antennas and are not suitable for elliptical aperture. Therefore, a trial and error method is developed in the prior art to optimize the orofacial field and the transition function, but the method is very inefficient, and it is difficult to quickly find the optimal orofacial field distribution and the transition function.
Disclosure of Invention
In view of this, the present invention provides a method for designing an elliptical beam cassegrain antenna, which can solve the problem of fast optimization with fewer control parameters, and can be used for fast optimization design of an elliptical beam antenna with high efficiency, low side lobe, low cross polarization, and large axial ratio.
In order to achieve the purpose, the invention adopts the following technical scheme:
a design method of an elliptical beam Cassegrain antenna comprises the following steps:
(A1) Parameterizing the oral surface field function and the transition function in the long and short axis planes;
(A2) Forming population individuals by parameters of the mouth-face field function and the transition function, and performing population iteration based on a DEGL algorithm; in the iteration process, the first side lobe is constrained, and the efficiency of the elliptical beam antenna is optimized;
(A3) Shaping the antenna by using the optimal individual in the population of the last generation to obtain the optimal design of the elliptic wave beam Cassegrain antenna;
in the step (A2), each individual in the primary generation population is randomly generated, and the generation manner of each generation population includes the following steps:
(B1) Shaping the elliptic wave beam Cassegrain antenna by taking the aperture surface field function parameter and the transition function parameter of each individual in the prior generation population as variables to obtain a model of the antenna;
(B2) Carrying out simulation calculation on the antenna model by using a physical optical method and a physical diffraction method to obtain the efficiency and the first side lobe of the antenna model;
(B3) According to the efficiency and the first side lobe of the antenna model, the efficiency of the antenna is maximized, meanwhile, the first side lobe in a working frequency band is guaranteed to meet design requirements, a global optimal individual in a previous generation population is selected, and a neighborhood optimal individual corresponding to the individual is selected from the neighborhood of each individual in the previous generation population;
(B4) Aiming at each individual in the prior generation population, solving a mutation operator, a crossover operator and a selection operator of the individual according to the neighborhood optimal individual and the global optimal individual corresponding to the individual, and generating the next generation individual of the individual based on the selection operator.
Specifically, the oral surface field functions in the long and short axis planes in step (A1) are respectively:
wherein, F 90° (u) is the orofacial field function in the long axis plane, F 0° (u) is the orofacial field function in the short axis plane, F 90° (u) and F 0° (u) is a k-order NURBS orofacial field curve; omega i Is a weight factor, d i 、d′ i Respectively representing the ith control point coordinate in the long and short axis planes, N i,k (u) is a k-th order canonical B-spline basis function;
the transition function is a sinusoidal exponential function with only one parameter q:
the population individuals in the step (A2) are:
X＝[d 0 ,...,d i ,...,d n ,d′ 0 ,...,d′ i ,...,d′ n ,q]。
specifically, the specific manner of step (B1) is:
(B101) In shortIn the axial plane, an aperture surface field function in the minor axis plane and initial parameters including the minor axis diameter of the main reflecting surface, the minor axis diameter of the auxiliary reflecting surface, the irradiation angle of the feed source, the maximum irradiation angle, the focal ratio and the directional diagram of the feed source are calculated by applying the forming method of the Cassegrain antenna in a mode of solving partial differential equations to obtain a curve r of the auxiliary reflecting surface in the minor axis plane 0° (θ)；
(B102) In the long axis plane, the shaping method of the Cassegrain antenna is applied by the mouth surface field function in the long axis plane and the initial parameters including the major axis diameter of the main reflecting surface, the major axis diameter of the auxiliary reflecting surface and the same optical path as in the short axis plane, and the curve r of the auxiliary reflecting surface in the long axis plane is solved by solving the partial differential equation set 90° (θ)；
(B103) By the sub-reflecting surface curve r in the long and short axis planes 90° (theta) and r 0° (theta) is a generatrix passing through a sine exponential function
Determining the sub-reflecting surface curved surface between the long and short axis planes:
obtaining the curved surface coordinate of the whole subreflector through two times of mirror symmetry;
(B104) And (3) solving a main reflecting surface by applying a reflection law and an aplanatic principle in a three-dimensional space, completing the rapid shaping of the elliptic beam Cassegrain antenna, and obtaining the model of the antenna.
Specifically, the diameter of the major axis of the sub-reflecting surface in the step (B102) is selected by a gradient step zero-finding method, and the specific method is as follows:
setting a threshold value epsilon for the major axis diameter D of the sub-reflecting surface s90° Carrying out iteration:
wherein k is iteration number, and Δ P is r under current iteration number 90° (0) And r 0° (0) Distance between | r 90° (0)-r 0° (0)|；
After a plurality of iterations until delta P is less than or equal to epsilon, D at the moment s90° The major axis diameter of the selected sub-reflecting surface is obtained.
Specifically, the mode of selecting the optimal individual in the step (B3) is:
constraining the first side lobe:
constructing an objective function:
wherein X is the population individual, eta n For the efficiency of the antenna at the nth frequency point, N is the total number of frequency points, PSLL0 n And PSLL90 n A pitching first side lobe and an azimuth first side lobe of the nth frequency point are respectively;
establishing a fitness function of the target function:
where K is the majority of the processing constraints;
for population individuals meeting Fit (X) epsilon (0, 1), the individuals with the minimum Fit (X) value are the optimal individuals.
Specifically, the way of calculating the mutation operator in step (B4) is:
from the ith individual X in the G generation population i,G Corresponding neighborhood optimal individual X n_best,G And globally optimal individual X g_best,G Based on the above, neighborhood vectors are constructed respectively
And a global vector
Constructing a mutation operator by the neighborhood vector and the global vector: v i,G ＝ω·g i,G +(1-ω)·L i,G ，
Wherein, alpha and beta are scaling factors, X p,G 、X q,G 、
And omega is a weight factor which is randomly selected from the G generation population, the value range is between 0 and 1, and the weight factor omega is linearly increased from a preset minimum weight factor to a preset maximum weight factor along with the increase of the evolution generation G.
Compared with the prior art, the invention has the following advantages:
1. the method carries out optimization design on the elliptical beam Cassegrain antenna based on a DEGL algorithm (Differential Evolution with Global and Local neighbor based on a Differential Evolution algorithm of Global and neighborhood), overcomes the defect of the existing shaping elliptical beam antenna trial and error method optimization, can balance the contradiction between Global optimization and rapid convergence, can efficiently realize the performance optimization of low side lobe, high efficiency, wide frequency band and the like of the elliptical beam antenna, and can provide the optimal orofacial field distribution and transition function suitable for the elliptical beam antenna.
2. Furthermore, the invention applies a gradient stepping zero-searching method in antenna modeling, and can realize the rapid shaping design of the elliptical beam antenna. The gradient information is introduced into the iteration step, the iteration times can be greatly reduced, the delta P can reach the precision of less than 1/1000mm after 3-4 iterations, and compared with the classical algorithm which needs 30-40 iterations, the efficiency can be improved by 10 times.
3. Furthermore, the invention adopts NURBS curve to parameterize the oral surface field in the long and short axis planes and adopts sine index function to parameterize the transition function, thus, the control freedom of the elliptical aperture oral surface field can be expanded only by using less parameters, and simultaneously, the speed of optimizing convergence is also improved.
In a word, the method has the advantages of novel concept, simplicity, practicability and higher operation efficiency, can obviously improve the design performance of the elliptical beam Cassegrain antenna, and is an important improvement on the prior art.
Drawings
Fig. 1 is a front view of the primary and secondary reflective surfaces of an elliptical beam antenna in an embodiment of the present invention.
Fig. 2 is a top view of the primary and secondary reflective surfaces of the elliptical beam antenna in an embodiment of the present invention.
Fig. 3 is an enlarged view of the sub-reflecting surface of fig. 2.
Fig. 4 is a flowchart of fast shaping of an elliptical beam antenna according to an embodiment of the present invention.
Fig. 5 is a general flow diagram of an elliptical beam antenna design in an embodiment of the present invention.
In the figure, 1, main surface, 2, minor surface, 3, minor axis plane
Upper subsidiary reflecting surface curve, 4, major axis plane
Upper sub-reflector curve.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
A design method of an elliptical beam Cassegrain antenna comprises the following steps:
(A1) Parameterizing the orofacial field functions and the transition functions in the long and short axis planes:
the oral surface field functions in the long and short axis planes are expressed by using the control point parameters of two non-uniform rational B-spline curves (namely NURBS curves), which are respectively:
in the formula, F 90° (u) and F 0° The functional form of (u) is k times NURBS orofacial field curve, where ω is i Is a weight factor, d i 、d′ i Respectively, the ith control point coordinate in the long and short axis planes. N is a radical of hydrogen i,k (U) is a k-th order canonical B-spline basis function, which can be represented by the node vector U = [ U ] 0 ,u 1 ,...u i ,...u n+k+1 ]According to the Deboolean-Corx recursion formula
Obtaining;
the transition function is a sinusoidal exponential function with only one parameter q:
by parameterizing the control points d of the orofacial field in the long and short axis planes i 、d′ i And a transition function parameter q, forming an optimized vector of the elliptical wave number antenna:
X＝[d 0 ,...,d i ,...,d n ,d′ 0 ,...,d′ i ,...,d′ n ,q]。
(A2) Taking the optimized vector of the elliptical wave number antenna as a population individual, and performing population iteration based on a DEGL algorithm; and in the iteration process, the first side lobe is constrained, and the efficiency of the elliptical beam antenna is optimized.
The optimal design of the elliptical beam antenna aims at maximizing the efficiency of the antenna while ensuring that the first side lobe in the operating frequency band meets the design requirements, and the problem can be expressed as a minimization problem of the following objective function:
wherein eta is n For the efficiency of the antenna at the nth frequency point, N is the total number of frequency points.
The efficiency of the elliptical beam antenna is obtained by the antenna Gain, the wavelength lambda and the equivalent area S of the elliptical beam antenna:
at the same time, the constraint condition is also satisfied:
in the formula, PSLL0 n And PSLL90 n The first pitching side lobe and the first azimuth side lobe of the nth frequency point are respectively.
The above problems are converted into fitness functions by adopting an accurate penalty function method
To solve the problem of unconstrained optimization. K is the large number of processing constraints, the fitness is a large value when the first side lobe does not meet the constraints, otherwise, fit (X) belongs to (0, 1), and the minimum Fit (X) corresponds to the optimal individual.
(A3) After multiple iterations, the optimal individual in the last generation of population is the optimal design of the elliptical beam Cassegrain antenna.
In the step (A2), each individual in the primary population is randomly generated, and thereafter, each offspring population is generated as follows:
(B1) Shaping the elliptic wave beam Cassegrain antenna by taking an aperture surface field function and a transition function of each individual in the prior generation population as variables to obtain an antenna model;
(B2) Carrying out simulation calculation on the antenna model by using a PO physical optical method and a PTD physical diffraction method to obtain the accurate efficiency and the first side lobe of the antenna model;
(B3) Aiming at the G generation group according to the efficiency and the first side lobe of the antenna model
The ith individual X in (1) i,G (i =1,2, \8230;, NP), defining a radiusIs the neighborhood of R (0 < R < (NP-1)/2), then the neighborhood population is { X i-R,G ,X i,G ,…,X i+R,G }; selecting the optimal individual as the optimal individual in the neighborhood
At the same time, the population { X) in the whole G generation 1,G ,X 2,G ,…,X NP,G Selecting the optimal individual as the global optimal individual X g_best,G 。
(B4) Obtaining the optimal individual X of the neighborhood from (B3) aiming at each individual in the prior generation population n_best,G And G-th generation globally optimal individual X g_best,G Respectively building neighborhood vectors
And global vector of G generation
Constructing mutation operator from the two
Wherein, alpha and beta are scaling factors, X p,G 、X q,G 、
For randomly selected individuals in the G generation population, a weight factor
Will increase with evolution algebra G from the minimum weight factor omega min To the maximum weight factor omega max The linear increment is carried out, and the value range of the weight factor omega is between 0 and 1.
Then, the crossover factor CR is selected to obtain a crossover operator and a selection operator, so as to generate the next generation of individuals of the individuals. The concepts of crossover operators and selection operators are prior art and will not be described further herein.
As shown in fig. 1 to 4, in the step (B1), the method for designing the fast shaping of the elliptical beam cassegrain antenna includes:
(B101) XOZ plane (i.e. short axis plane) in O-XYZ rectangular coordinate system
) In (A1), the short-axis orofacial field function F parameterized by the parameters 0° (u) and initial parameters: minor axis diameter D of main reflector m0° Minor axis diameter D of the subreflector s0° Feed source irradiation angle theta m Maximum irradiation angle θ m The focal length ratio tau and the feed source directional diagram f (theta) are solved by applying the shaping method of the Cassegrain antenna
Calculating to obtain a sub-reflecting surface curve r in the short axis plane 0° (θ) the first sub-reflector bus bar 3 of the antenna.
(B102) Similarly, in the YOZ plane (i.e. long axis plane) of O-XYZ rectangular coordinate system
) In (A1), the parameterized long-axis orofacial field function F 90° And initial parameters: major axis diameter D of main reflector m90° Minor reflecting surface major axis diameter D s90° And calculating a sub-reflector curve r in the major axis plane by using the same optical path Ck in the minor axis plane and the shaping method of the Cassegrain antenna 90° (θ) is the second subreflector bus 4 of the antenna.
In this step, the key difficulty is to select the appropriate D s90° To ensure that the vertices of the plane and the vertices in the minor axis plane coincide as much as possible (i.e., satisfy Δ P = | r) 90° (0)-r 0° (0) | ≦ epsilon), thereby facilitating modeling of the subreflector. For this purpose, a gradient step zero-searching method is applied to establish an automatic fast iterative loop, and k iterations are performed
Until delta P is less than or equal to epsilon, D can be determined s90° 。
In the iterative formula, the iteration times can be greatly reduced by introducing gradient information, only 3-4 iterations are needed, and the precision of less than 1/1000mm can be achieved by delta P. Compared with the classical algorithm which needs to iterate 30-40 times, the efficiency of the method can be improved by 10 times.
(B103) After two sub-reflecting surface generatrices 3 and 4 are determined, a transition function parameterized in (A1) is introduced
The curved surface of the auxiliary reflecting surface between the long and short axis planes can be determined:
and then, obtaining the curved surface coordinates of the whole subreflector through two times of mirror symmetry.
And finally, the main reflecting surface can be obtained by applying the reflection law and the aplanatic principle in the three-dimensional space, and the rapid shaping of the elliptical beam Cassegrain antenna can be completed.
The shaping process of the above-mentioned elliptical beam antenna is shown in fig. 4.
Fig. 5 shows a whole antenna design process, and by programming a suitable program, processes such as automatic modeling, simulation calculation, data analysis, population iterative operation, and the like can be implemented. And (3) shaping the antenna by the optimal individual of the last generation according to the mode of the step (B1) until the maximum generation of the population is reached, thus finishing the optimal design of the elliptical beam Cassegrain antenna.
By the method, the 630 mm-1150 mm-caliber elliptical beam Cassegrain antenna is designed, the aperture surface efficiency of the antenna can reach more than 64.6% and more than 68.9% respectively in a Ku frequency band and a Ka frequency band, the first side lobe of the short axis is lower than-15.1 dB, and the first side lobe of the long axis is lower than-16.1 dB. Compared with the literature (Liuxing Longng, dubiao, qin Shunyou, a low-profile high-efficiency large-axial-ratio elliptical beam antenna [ J ]. Radiowave science bulletin, 2011,26 (supplement): 505-508.), the first side lobe of the antenna obtained by the method is reduced by 2dB, the frequency band is expanded to Ka/Ku dual-frequency band, and the efficiency is improved by 2%. In addition, the equivalent diameter of the main reflecting surface of the antenna is 890mm, and compared with 851mm equivalent diameter of a standard elliptical beam antenna, the effective area is increased by 9.3%; meanwhile, the longitudinal height of the antenna is only 327mm, so that a large enough space is saved for the arrangement and layout of the rear-end feed network, and the whole antenna system is convenient to realize a low profile.
It should be understood that the above description of the embodiments of the present patent is only an exemplary description for facilitating the understanding of the patent scheme by the person skilled in the art, and does not imply that the scope of protection of the patent is only limited to these examples, and that a person skilled in the art can obtain more embodiments without any inventive step in the form of combining technical features, replacing technical features, adding more technical features, and the like, of the various embodiments listed in the patent, and all of these embodiments are within the scope of the patent claims, and therefore, these new embodiments should also be within the scope of protection of the patent.
Claims (1)
1. A design method of an elliptical beam Cassegrain antenna is characterized by comprising the following steps:
(A1) Parameterizing the oral surface field function and the transition function in the long and short axis planes;
(A2) Forming population individuals by parameters of the mouth-face field function and the transition function, and performing population iteration based on a DEGL algorithm; in the iteration process, the first side lobe is constrained, and the efficiency of the elliptical beam antenna is optimized;
(A3) Shaping the antenna by using the optimal individual in the population of the last generation to obtain the optimal design of the elliptic wave beam Cassegrain antenna;
in the step (A2), each individual in the primary generation population is randomly generated, and the generation manner of each generation population includes the following steps:
(B1) Shaping the elliptical beam Cassegrain antenna by taking the aperture surface field function parameter and the transition function parameter of each individual in the previous generation population as variables to obtain a model of the antenna;
(B2) Carrying out simulation calculation on the antenna model by using a physical optical method and a physical diffraction method to obtain the efficiency and the first side lobe of the antenna model;
(B3) According to the efficiency and the first side lobe of the antenna model, the efficiency of the antenna is maximized, meanwhile, the first side lobe in a working frequency band is guaranteed to meet design requirements, a globally optimal individual in a previous generation population is selected, and a neighborhood optimal individual corresponding to the individual is selected from the neighborhood of each individual in the previous generation population;
(B4) Aiming at each individual in the prior generation population, solving a mutation operator, a crossover operator and a selection operator of the individual according to the neighborhood optimal individual and the global optimal individual corresponding to the individual, and generating a next generation individual of the individual based on the selection operator;
the mouth surface field functions in the long and short axis planes in the step (A1) are respectively as follows:
wherein, F 90° (u) is the orofacial field function in the plane of the major axis, F 0° (u) is the orofacial field function in the short axis plane, F 90° (u) and F 0° (u) is a k-order NURBS orofacial field curve; omega i Is a weight factor, d i 、d′ i Respectively representing the ith control point coordinate in the long and short axis planes, N i,k (u) k-th order normalized B-spline basis functions;
the transition function is a sinusoidal exponential function with only one parameter q:
the population individuals in the step (A2) are as follows:
X＝[d 0 ,...,d i ,...,d n ,d′ 0 ,...,d′ i ,...,d′ n ,q]；
the specific mode of the step (B1) is as follows:
(B101) In the short axis plane, an aperture surface field function in the short axis plane and initial parameters including the main reflecting surface short axis diameter, the auxiliary reflecting surface short axis diameter, the feed source irradiation angle, the maximum irradiation angle, the focal diameter ratio and the feed source directional diagram are calculated by applying a forming method of the Cassegrain antenna and solving a partial differential equation set to obtain an auxiliary reflecting surface curve r in the short axis plane 0° (θ)；
(B102) In the major axis plane, the shaping method of the Cassegrain antenna is applied by the mouth surface field function in the major axis plane and the initial parameters including the major axis diameter of the main reflecting surface, the major axis diameter of the auxiliary reflecting surface and the same optical path as that in the minor axis plane, and the curve r of the auxiliary reflecting surface in the major axis plane is obtained by solving the partial differential equation set 90° (θ)；
(B103) By the sub-reflecting surface curve r in the long and short axis planes 90° (theta) and r 0° (theta) is a generatrix passing through a sine exponential function
Determining the sub-reflecting surface curved surface between the long and short axis planes:
obtaining the curved surface coordinate of the whole auxiliary reflecting surface through two times of mirror symmetry;
(B104) Applying a reflection law and an aplanatic principle to obtain a main reflecting surface in a three-dimensional space, and completing the rapid shaping of the elliptical beam Cassegrain antenna to obtain a model of the antenna;
the diameter of the major axis of the sub-reflecting surface in the step (B102) is selected by a gradient step zero-finding method, and the specific method is as follows:
setting a threshold value epsilon for the major axis diameter D of the sub-reflecting surface s90° Carrying out iteration:
wherein k is the number of iterations, and Δ P is r under the current number of iterations 90° (0) And r 0° (0) Distance between | r 90° (0)-r 0° (0)|；
After a plurality of iterations until delta P is less than or equal to epsilon, D s90° The major axis diameter of the selected subreflector is obtained;
the mode of selecting the optimal individual in the step (B3) is as follows:
constraining a first side lobe:
constructing an objective function:
wherein X is a population individual, h n For the efficiency of the antenna at the nth frequency point, N is the total number of frequency points, PSLL0 n And PSLL90 n A pitching first side lobe and an azimuth first side lobe of the nth frequency point are respectively;
establishing a fitness function of the target function:
where K is the majority of the processing constraints;
for population individuals meeting Fit (X) epsilon (0, 1), the individual with the minimum Fit (X) value is the optimal individual;
the way of calculating the mutation operator in the step (B4) is:
from ith individual X in G generation population i,G Corresponding neighborhood optimal individual X n_best,G And globally optimal individual X g_best,G Based on the above, neighborhood vectors are constructed respectively
And a global vector
Constructing a mutation operator by the neighborhood vector and the global vector: v i,G ＝ω·g i,G +(1-ω)·L i,G ，
Wherein, alpha and beta are scaling factors, X p,G 、X q,G 、
And omega is a weight factor which is randomly selected from the G generation population, the value range is between 0 and 1, and the weight factor omega is linearly increased from a preset minimum weight factor to a preset maximum weight factor along with the increase of the evolution generation G.
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